This will contain my notes on Iwasawa-Tate theory. This will be done first for number fields and simple algebras (a la Weil), giving some number theoretic results. The meat of these notes is a study of the Standard L-functions for GL(n). We extend this to arbitary simple algebras (a la Godement/Jacquet). This is a long term project. As of now, I have basically completed the first case. There ar...

We prove one inclusion of the Iwasawa Main Conjecture, and Bloch-Kato conjecture in analytic rank 0, for symmetric cube a level 1 modular form.

The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...